Fitting Heavy-Tailed Distributions to Mortality Indexes for Longevity Risk Forecasts

Abstract

Modeling and predicting mortality rates are crucial for managing and mit- igating longevity risk in pension funds. To address the impacts of extreme mortality events in forecasting, researchers suggest directly fitting a heavy-tailed distribution to the residuals in modeling mortality indexes. Since the true mortality indexes are unobserved, this fitting relies on the estimated mortality indexes containing measure- ment errors, leading to estimation biases in standard inferences within the actuarial literature. In this paper, the empirical characteristic function (ECF) technique is em- ployed to fit heavy-tailed distributions to the time series residuals of mortality indexes and normal distributions to the measurement errors. Through a simulation study, we empirically validate the consistency of our proposed method and demonstrate the im- portance and challenges associated with making inferences in the presence of mea- surement errors. Upon analyzing publicly available mortality datasets, we observe instances where mortality indexes may follow highly heavy-tailed distributions, even exhibiting an infinite mean. This complexity adds a layer of difficulty to the statistical inference for mortality models.

Keywords

Characteristic function / Lee-Carter model / mortality rates / unit root model